Pointwise bi-slant Riemannian maps ($\mathcal{PBSRM}$) from almost Hermitian manifolds

Abstract

In 2022, the notion of pointwise slant Riemannian maps were introduced by Y. G\"{u}nd\"{u}zalp and M. A. Akyol (Journal of Geometry and Physics, 179, 104589, 2022) as a natural generalization of slant Riemannian maps, slant Riemannian submersions, slant submanifolds. As a generalization of pointwise slant Riemannian maps and many subclasses notions (see: Figure 2), we introduce {\textit pointwise bi-slant Riemannian maps (briefly, $\mathcal{PBSRM}$)} from almost Hermitian manifolds to Riemannian manifolds, giving a figure which shows the subclasses of the map and a non-trivial (proper) example and investigate some properties of the map, we deal with their properties: the J-pluriharmonicity, the J-invariant, and the totally geodesicness of the map. Finally, we study some curvature relations in complex space form, involving Chen inequalities and Casorati curvatures for $\mathcal{PBSRM}$, respectively.